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Efficient Convexification Strategy for Generalized Geometric Programming Problems

Author

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  • Hao-Chun Lu

    (Department of Information Management, Fu Jen Catholic University, Xinzhuang, New Taipei City, 24205 Taiwan)

  • Liming Yao

    (Business School, Sichuan University, 610065 Chengdu, China)

Abstract

Generalized geometric programming (GGP) problems consist of a signomial being minimized in the objective function subject to signomial constraints, and such problems have been utilized in various fields. After modeling numerous applications as GGP problems, solving them has become a significant requirement. A convex underestimator is considered an important concept to solve GGP problems for obtaining the global minimum. Among convex underestimators, variable transformation is one of the most popular techniques. This study utilizes an estimator to solve the difficulty of selecting an appropriate transformation between the exponential transformation and power convex transformation techniques and considers all popular types of transformation techniques to develop a novel and efficient convexification strategy for solving GGP problems. This proposed convexification strategy offers a guide for selecting the most appropriate transformation techniques on any condition of a signomial term to obtain the tightest convex underestimator. Several numerical examples in the online supplement are presented to investigate the effects of different convexification strategies on GGP problems and demonstrate the effectiveness of the proposed convexification strategy with regard to both solution quality and computation efficiency.

Suggested Citation

  • Hao-Chun Lu & Liming Yao, 2019. "Efficient Convexification Strategy for Generalized Geometric Programming Problems," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 226-234, April.
    • Handle: RePEc:inm:orijoc:v:31:y:2019:i:2:p:226-234
    DOI: 10.1287/ijoc.2018.0850
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    References listed on IDEAS

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    1. Han-Lin Li & Hao-Chun Lu, 2009. "Global Optimization for Generalized Geometric Programs with Mixed Free-Sign Variables," Operations Research, INFORMS, vol. 57(3), pages 701-713, June.
    2. Jung-Fa Tsai & Ming-Hua Lin, 2011. "An Efficient Global Approach for Posynomial Geometric Programming Problems," INFORMS Journal on Computing, INFORMS, vol. 23(3), pages 483-492, August.
    3. Stephen P. Boyd & Seung-Jean Kim & Dinesh D. Patil & Mark A. Horowitz, 2005. "Digital Circuit Optimization via Geometric Programming," Operations Research, INFORMS, vol. 53(6), pages 899-932, December.
    4. S. Caratzoulas & C. A. Floudas, 2005. "Trigonometric Convex Underestimator for the Base Functions in Fourier Space," Journal of Optimization Theory and Applications, Springer, vol. 124(2), pages 339-362, February.
    5. Hao-Chun Lu & Han-Lin Li & Chrysanthos Gounaris & Christodoulos Floudas, 2010. "Convex relaxation for solving posynomial programs," Journal of Global Optimization, Springer, vol. 46(1), pages 147-154, January.
    6. Jung, Hoon & Klein, Cerry M., 2001. "Optimal inventory policies under decreasing cost functions via geometric programming," European Journal of Operational Research, Elsevier, vol. 132(3), pages 628-642, August.
    7. Han-Lin Li & Hao-Chun Lu & Chia-Hui Huang & Nian-Ze Hu, 2009. "A Superior Representation Method for Piecewise Linear Functions," INFORMS Journal on Computing, INFORMS, vol. 21(2), pages 314-321, May.
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    Cited by:

    1. Lu, Hao-Chun, 2020. "Indicator of power convex and exponential transformations for solving nonlinear problems containing posynomial terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).

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